Accelerating boundary integral equation method using a special-purpose computer

We present a new solution to accelerate the boundary integral equation method (BIEM). The calculation time of the BIEM is dominated by the evaluation of the layer potential in the boundary integral equation. We performed this task using MDGRAPE-2, a special-purpose computer designed for molecular dynamics simulations. MDGRAPE-2 calculates pairwise interactions among particles (e.g. atoms and ions) using hardwired-pipeline processors. We combined this hardware with an iterative solver. During the iteration process, MDGRAPE-2 evaluates the layer potential. The rest of the calculation is performed on a conventional PC connected to MDGRAPE-2. We applied this solution to the Laplace and Helmholtz equations in three dimensions. Numerical tests showed that BIEM is accelerated by a factor of 10–100. Our rather naive solution has a calculation cost of O(N2 × Niter), where N is the number of unknowns and Niter is the number of iterations